Weak convergence of explicit extragradient algorithms for solving equilibirum problems
Abstract This paper aims to propose two new algorithms that are developed by implementing inertial and subgradient techniques to solve the problem of pseudomonotone equilibrium problems. The weak convergence of these algorithms is well established based on standard assumptions of a cost bi-function....
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-11-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13660-019-2233-1 |
| _version_ | 1818116125662117888 |
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| author | Habib ur Rehman Poom Kumam Yeol Je Cho Pasakorn Yordsorn |
| author_facet | Habib ur Rehman Poom Kumam Yeol Je Cho Pasakorn Yordsorn |
| author_sort | Habib ur Rehman |
| collection | DOAJ |
| description | Abstract This paper aims to propose two new algorithms that are developed by implementing inertial and subgradient techniques to solve the problem of pseudomonotone equilibrium problems. The weak convergence of these algorithms is well established based on standard assumptions of a cost bi-function. The advantage of these algorithms was that they did not need a line search procedure or any information on Lipschitz-type bifunction constants for step-size evaluation. A practical explanation for this is that they use a sequence of step-sizes that are updated at each iteration based on some previous iterations. For numerical examples, we discuss two well-known equilibrium models that assist our well-established convergence results, and we see that the suggested algorithm has a competitive advantage over time of execution and the number of iterations. |
| first_indexed | 2024-12-11T04:17:33Z |
| format | Article |
| id | doaj.art-4c4d852398bc4115839defdb5425e4bb |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-12-11T04:17:33Z |
| publishDate | 2019-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-4c4d852398bc4115839defdb5425e4bb2022-12-22T01:21:13ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-11-012019112510.1186/s13660-019-2233-1Weak convergence of explicit extragradient algorithms for solving equilibirum problemsHabib ur Rehman0Poom Kumam1Yeol Je Cho2Pasakorn Yordsorn3Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT)Department of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT)Department of Mathematics Education, Gyeongsang National UniversityDepartment of Mathematics, King Mongkut’s University of Technology Thonburi (KMUTT)Abstract This paper aims to propose two new algorithms that are developed by implementing inertial and subgradient techniques to solve the problem of pseudomonotone equilibrium problems. The weak convergence of these algorithms is well established based on standard assumptions of a cost bi-function. The advantage of these algorithms was that they did not need a line search procedure or any information on Lipschitz-type bifunction constants for step-size evaluation. A practical explanation for this is that they use a sequence of step-sizes that are updated at each iteration based on some previous iterations. For numerical examples, we discuss two well-known equilibrium models that assist our well-established convergence results, and we see that the suggested algorithm has a competitive advantage over time of execution and the number of iterations.http://link.springer.com/article/10.1186/s13660-019-2233-1Equilibrium problemExtragradient methodLipschitz-type conditionsNash–Cournot equilibrium model of electricity markets |
| spellingShingle | Habib ur Rehman Poom Kumam Yeol Je Cho Pasakorn Yordsorn Weak convergence of explicit extragradient algorithms for solving equilibirum problems Journal of Inequalities and Applications Equilibrium problem Extragradient method Lipschitz-type conditions Nash–Cournot equilibrium model of electricity markets |
| title | Weak convergence of explicit extragradient algorithms for solving equilibirum problems |
| title_full | Weak convergence of explicit extragradient algorithms for solving equilibirum problems |
| title_fullStr | Weak convergence of explicit extragradient algorithms for solving equilibirum problems |
| title_full_unstemmed | Weak convergence of explicit extragradient algorithms for solving equilibirum problems |
| title_short | Weak convergence of explicit extragradient algorithms for solving equilibirum problems |
| title_sort | weak convergence of explicit extragradient algorithms for solving equilibirum problems |
| topic | Equilibrium problem Extragradient method Lipschitz-type conditions Nash–Cournot equilibrium model of electricity markets |
| url | http://link.springer.com/article/10.1186/s13660-019-2233-1 |
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